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DNA-testing for immigration cases: The risk of erroneous conclusions

Andreas O. Karlsson a,*, Gunilla Holmlund a, Thore Egeland b, Petter Mostad c

a The National Board of Forensic Medicine, Department of Forensic Genetics and Forensic Toxicology, Artillerigatan 12, SE-581 33 Linkoping, Swedenb Department of Medical Genetics, Ullevaal University Hospital, NO-0407 Oslo, Norway

c Department of Biostatistics, Institute of Basic Medical Sciences, University of Oslo, P.O. Box 1122, Blindern, NO-0317 Oslo, Norway

Received 30 August 2006; received in revised form 27 November 2006; accepted 3 December 2006

Abstract

Making the correct decision based on results from DNA analyses and other information in family reunification cases can be complicated for a

number of reasons. These include stratified populations, cultural differences in family constellations, families with different population origin, and

complicated family relations giving complex pedigrees. The aim of this study was to analyze the risk of erroneous conclusions in immigration cases

and to propose alternative procedures to current methods to reduce the risk of making such errors. A simulation model was used to study different

issues. For simplicity, we focus on cases which can be formulated as questions about paternity. We present an overview of error rates (of falsely

included men as the true father and of falsely excluded true fathers) for fairly standard computations, and we show how these are affected by

different factors. For example, adding more DNA markers to a case will decrease the error rates, as will the inclusion of more children. We found

that using inappropriate population frequency databases had just minor effects on the error rates, but the likelihood ratios varied from an

underestimation of 100 times up to an overestimation of 100,000 times. To reduce the risk of falsely including a man related to the true father we

propose a more refined prior including five hypotheses instead of the two normally used. Simulations showed that this method gave reduced error

rates compared with standard computations, even when the prior does not exactly correspond to reality.

# 2007 Elsevier Ireland Ltd. All rights reserved.

Keywords: Immigration casework; Bayesian; Mutation model; Simulation

www.elsevier.com/locate/forsciint

Forensic Science International xxx (2007) xxx–xxx

1. Introduction

The use of DNA analysis in forensic casework has

revolutionized the area of forensic science. Suspects can be

linked to crime scenes, victims of mass disasters such as

airplane crashes can be identified and questions of disputed

paternity can be solved [1,2]. DNA can also be used as a tool in

immigrations cases, which is the focus of this paper.

Immigration casework involves family reunification and

often consists of a man who would like to be reunified with his

wife and children. In such cases, the question is whether a given

man, the alleged father (AF) is the true father (TF) of a number

of children. The maternity of the alleged mother is usually not

questioned. In general, all stated relationships could be

questioned, and a range of different pedigrees could be used

as hypotheses. Methods presented in this paper could be

* Corresponding author. Tel.: +46 13 31 58 70; fax: +46 13 13 60 05.

E-mail address: andreas.karlsson@rmv.se (A.O. Karlsson).

0379-0738/$ – see front matter # 2007 Elsevier Ireland Ltd. All rights reserved.

doi:10.1016/j.forsciint.2006.12.015

Please cite this article in press as: A.O. Karlsson et al., DNA-testing for im

(2007), doi:10.1016/j.forsciint.2006.12.015

directly extended to such situations. However, as most cases in

practice seem adequately represented by the paternity

perspective,1 this will be the focus of our paper. Treating

immigration cases as paternity cases they have, however, some

characteristics of their own, like frequently involving popula-

tions where knowledge of allele frequencies may be

inadequate. Also, there may be varying degrees of consangui-

nity making it reasonable to analyze alternative pedigrees.

Our aim was to study the risk of erroneous conclusions in

immigration cases and to propose alternatives to current

methods to reduce the risk of making such errors.2 In a paternity

case a decision can comprise two types of errors. Here we

define them as ‘‘exclusion errors’’ and ‘‘inclusion errors’’,

meaning a false exclusion, respectively, a false inclusion, of the

1 Note that cases where maternity but not paternity is in question are entirely

similar, by symmetry.2 Note our use of the term error: this paper does not discuss DNA-typing

errors, calculation or typing errors or the like. An error is for us an erroneous

conclusion in the question underlying the immigration case.

migration cases: The risk of erroneous conclusions, Forensic Sci. Int.

A.O. Karlsson et al. / Forensic Science International xxx (2007) xxx–xxx2

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AF from paternity. There will always be a balance between

these errors and the goal is to reduce them simultaneously.

These error rates together with likelihood ratios are used for

measuring the impact of different parameters in the statistical

computations.

An important issue in all paternity cases is how to handle

inconsistencies between the profiles of an AF and a child. This

issue is not specific neither for paternity nor immigration

casework, but since we in this paper deal with describing and

evaluating the possibilities of misclassification in immigration

cases, mutations might have an impact. One approach to deal

with this is to use a probabilistic mutation model. Different

models have been proposed [3–5] but none have yet been

generally adopted. An alternative way to account for

inconsistencies is to exclude them from the likelihood

calculations and instead set a limit of a maximum of one or

two inconsistencies between the profiles of an AF and a child

(later referred as 1-incon and 2-incon, respectively) before

rejecting paternity. The rationale behind the approach would be

that it should have comparable error rates with the first

alternative, but without the need to decide on a mutation model.

As different laboratories use different approaches in cases

including inconsistencies, it is relevant to study our main

questions in the context of these different approaches.

In addition to studying levels of error rates in standard cases,

we also study how these rates are affected by a number of

factors, such as the number of DNA markers used, the number

of children involved, and the use of inappropriate population

databases. Finally, we propose and study a computational

method that explicitly takes into account the possibility of the

AF being a close relative of the TF.

All studies were done using simulations. Simulation of

families and their DNA profiles gives the opportunity to rather

simply investigate different issues and also test the impact of

changing the model and thus the influence of different

parameters. This can ensure robustness of our results in

relation to uncertainties about true population frequencies,

possible familial relations, etc. With the limited number of

thoroughly investigated real cases, it is difficult to see an

alternative to using simulations.

2. Materials and methods

Different methods for paternity calculations can most easily be understood

in a Bayesian framework [6,7]. Let H0 be the hypothesis that AF is the TF, and

let H1 be the complementary possibility that he is not. Assuming that the

likelihoods LR = P(datajH0)/P(datajH1) 3 and P(datajH1) can be calculated, and

writing LR = P(datajH0)/P(datajH1) for the likelihood ratio, Bayes formula on

odds form gives

p1

1� p1

¼ LRp0

1� p0

or

p1 ¼LRð p0=ð1� p0ÞÞ

LRð p0=ð1� p0ÞÞ þ 1

3 The notation P(datajH0) means: the probability of observing the given data

given that the hypothesis H0 is true.

Please cite this article in press as: A.O. Karlsson et al., DNA-testing for im

(2007), doi:10.1016/j.forsciint.2006.12.015

where p0 is the prior probability for H0 and p1 is the corresponding posterior

probability P(datajH1). When we make the assumption p0 = 0.5, we define

W = p1, and we get the Essen–Moller’s formula

W ¼ LR

LRþ 1¼ PI

PIþ 1

where PI is the paternity index. We see that W, PI and LR are all directly related,

and for any fixed p0, there is a direct relationship between LR and P1. Below, we

will fix p0 = 0.5.

In practice, results from paternity calculations are most often used to make a

decision: AF is declared as the TF, or not. It is then important to avoid both that

the AF is falsely excluded as TF (exclusion error), and that the AF is falsely

included as TF (inclusion error). Let CI and CII be the ‘‘costs’’ of these two types

of errors. The expected cost of rejecting AF as TF is then equal to CI times the

probability that H0 is true, and the posterior expected cost becomes p1CI.

Similarly, the posterior expected cost of accepting AF as TF is (1 � p1)CII. It is

clear that the expected posterior cost is minimized when we declare AF as TF

whenever

p1CI�ð1� p1ÞCII

or equivalently

p1�1

ðCI=CIIÞ þ 1

Below, we will use the assumption that CI = CII, corresponding to a cutoff value

for pI at 50%. Using this cutoff will then minimize the expected sum of the error

rates.

It remains to be discussed how the likelihoods P(datajH0) and P(datajH1)

can be computed. In practice, we must make simplifying assumptions. In this

paper, we will use the following as our basic computational method, and an

example of a fairly standard procedure: When computing P(datajH0), we

assume that TF is a completely unrelated person, and that, when more than

one child is involved, he is the father of all the children. A Swedish allele

database (n = 300 individuals) is used to estimate frequencies. New, not earlier

seen alleles are added to the frequency databases with a default frequency of 5/

2n, where n is the number of individuals in the database [8]. Calculations of

likelihoods are done using the Familias program (http://www.nr.no/familias,

[9]) with mutation models explained later. We will also consider the common

procedure where loci with an inconsistency between the AF and the child are

simply removed from the computations. If the number of inconsistent loci is

above a maximum of either one or two loci, the AF is declared not to be the TF;

otherwise, the results from the reduced computations are used. This avoids the

specification of a mutation model.

If the likelihood computations correspond directly to (simulated) reality, we

saw above how using a cutoff for pI at 50% would minimize the sum of the error

rates. However, in what we will use as our two hypotheses standard procedure,

we use the cutoff 99.99%. The reason is that one suspects there are cases where a

close relative of TF is declared to be the true father. In such cases, the LR can

often be high, although usually lower than when AF is the TF. The high cutoff

value is meant to compensate for this.

However, when there is prior knowledge that there is a possibility for a close

relative of the AF to be the TF, and if it is possible to formulate this knowledge

into a precise prior, it is better to base the decision on the actual posterior for

such a model, and use a cutoff at 50%, than to use an ad-hoc adjustment. Thus,

we propose the following method:

We split the hypothesis H1 into four different hypotheses:

H1a. TF is the brother of AF.

H1b. TF is the father of AF.4

H1c. TF is the half-brother of AF.

4 The alternative that TF is the son of AF is not included separately, as it

would give exactly the same likelihood as when TF is the father of AF, except

for some very small differences with some mutation models.

migration cases: The risk of erroneous conclusions, Forensic Sci. Int.

Fig. 1. Error rate as a function of the cutoff value. The exclusion error, the

inclusion error and the total error were calculated for standard trios (mother,

child and AF). The bars represent 95% confidence intervals for simulation

uncertainty.

A.O. Karlsson et al. / Forensic Science International xxx (2007) xxx–xxx 3

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H1d. TF is unrelated to AF.

The likelihood P(datajH1) is then computed as

PðdatajH1Þ ¼ 0:25PðdatajH1aÞ þ 0:25PðdatajH1bÞ þ 0:25PðdatajH1cÞ

þ 0:25PðdatajH1dÞ

The weights 0.25 above are arbitrarily chosen, and could be more accurately

set in actual cases. Our goal here is to show that even using such arbitrarily

chosen weights results in a better performance than the ad-hoc adjustment of the

cutoff value used in the two hypotheses standard procedure.

2.1. Simulation study

To investigate the sizes of error rates, and to study how these rates are

affected by discrepancies between the simulated reality and assumptions used in

the likelihood computations, we performed a simulation study. STR data from

15 loci, including the 13 CODIS core loci plus D19S433 and D2S1338

(included in the Identifiler kit, Applied Biosystems) were used for the simula-

tion of DNA profiles. In some examples, profiles were generated with either 20

or 25 loci. This was done by reusing frequencies from 5 or 10 of the loci

mentioned above. Generally, a Swedish allele database (n = 300 individuals)

was used, but we also used an Iranian database (n = 150, [10]), a Somalian

database (n = 97, [11]) and a Rwandan database (n = 124, [12]) to study the

impact of using inappropriate allele databases in the computations. In the

simulation of a founder DNA profile the alleles at each locus were randomly

chosen based on the observed allele proportions in the database. An offspring

profile (a child) was generated using Mendelian heritage based on the profile of

the mother and the father. Mutations were allowed to occur when an offspring

profile was simulated. For this a decreasing mutation model was used [13] with

a m-gen5 of 0.1% per meiosis, locus, and generation (based on calculations from

[14]). In a test of the robustness of computations using mutation models, we also

used m-gen of 0.05 and 1%. Ninety percent of the mutations consisted of �1

repeat length differences and the rest were �2 repeats length mutations [5].

In all simulations the profiles of a mother, a father, and one or two children

were generated, and additionally a brother of the TF, a father of TF, a half-

brother of TF and a, to the TF, unrelated man. In the standard examples the TF

and the mother were assumed to be unrelated. When the impact of a relation

between the father and the mother was tested, they were simulated as first

cousins.

When simulating data under the H1 hypothesis, the four hypotheses H1a,

H1b, H1c, and H1d were used. In general, they were all assumed to be equally

probable, so that the error rate for inclusion errors could be computed as the

unweighted average rate of inclusion of AF as the TF under each of the

hypotheses H1a, H1b, H1c, and H1d. However, robustness of the results was also

considered by using weighted averages of these rates.

For each tested issue, 10,000 profiles were simulated for each person (TF,

brother of TF, father of TF, half-brother of TF and an unrelated man).

3. Results

3.1. Standard examples

Exclusion and inclusion error rates for standard trios (a

mother, child and AF), computed with Swedish allele data, are

shown in Fig. 1. The exclusion error rate increased with an

increasing cutoff level and the error rates of relatives or

unrelated being computed as the TF decreased as the cutoff

value increased. The most frequent inclusion error was the case

where the brother of the TF or the father of the TF were

5 The term m-gen denotes the mutation rate used in the simulation of profiles,

whereas the later used term m-comp denotes the mutation rate in likelihood

computation at a locus with an inconsistency between the AF and the child.

Please cite this article in press as: A.O. Karlsson et al., DNA-testing for im

(2007), doi:10.1016/j.forsciint.2006.12.015

included as the true father. The half-brother and the unrelated

man were very seldom included as the TF. The sum of the

exclusion and the inclusion error was the smallest between the

cutoff values 99.9 and 99.99% (Fig. 1).

Adding more genetic markers to these standard cases did

lower the error rates (Fig. 2), especially the exclusion error

which decreased more than the inclusion error (data not

shown). If one more child was added to the standard trio the

total error rate decreased almost 10 times, from 1.5 to 0.18%

with 99.99% cutoff level (Fig. 2).

The standard trios did not include any kinship relation

between the mother and the AF. In a separate test where the

father and mother were simulated to be first cousins there was

no, or very little, influence on the error rates (Fig. 2).

3.2. Impact of using or not using a mutation model

The computed probabilities were, in the standard examples,

based on a decreasing mutation model with the same m-gen and

m-comp (0.1%). The obtained results could in theory be due to

the use of an incorrect mutation model and also in real cases it is

not possible to select the true mutation rate for the likelihood

calculation. Only minor changes of the error rates occurred with

altered m-gen (0.05 and 0.1%) and m-comp (0.05, 0.1, 0.5 and

Fig. 2. The total error rates for trios with different conditions.

migration cases: The risk of erroneous conclusions, Forensic Sci. Int.

Fig. 3. The inclusion error rates from the different cases where a mutation model was or was not used.

A.O. Karlsson et al. / Forensic Science International xxx (2007) xxx–xxx4

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1%) (data not shown). When m-gen was set to 1% for all

markers the total error rates increased with more than 50%

(99.99% cutoff) using the same m-comp as above.

We also used a standard trio to test how the error rates

behaved when loci with inconsistencies were excluded from the

likelihood computations. The simulations showed that the

inclusion error rates became much higher using no mutation

model. Using 99.99% as a cutoff the inclusion error rates were

6, 1.6 and 0.6% for the cases with 1-incon, 2-incon and a

mutation model, respectively (Fig. 3). The exclusion error

showed an opposite pattern with low error rate when loci with

an inconsistency were excluded.

3.3. The effect of inappropriate allele databases

DNA profiles from families with a non-Swedish origin were

simulated to illustrate the impact of using an inappropriate

allele database for the likelihood calculations. Using Swedish

allele frequencies, instead of the correct one, generally

overestimated the likelihood ratios (medians: 4, 20 and 200

times; Iranian, Somalian and Rwandan allele frequencies,

Fig. 4. Box plot showing the ratio of the likelihood ratios obtained with

Swedish allele frequencies and the appropriate allele frequencies using simu-

lated profiles with either Iranian (median: �4 times), Somalian (�20 times) or

Rwandan (�200 times) origin. The likelihood ratio was computed with the

alleged father as the true father. The boxes have lines at the lower quartile,

median, and upper quartile values. The whiskers are lines extending from each

end of the boxes to show the extent of the rest of the data (covering 95%). The

whiskers value used was one.

Please cite this article in press as: A.O. Karlsson et al., DNA-testing for im

(2007), doi:10.1016/j.forsciint.2006.12.015

respectively) (Fig. 4). It is, however, important to notice that the

variance was quite large. For example, in the Rwanda case the

central 95% of the simulations covered the interval from an

underestimation of 100 times up to an overestimation of almost

100,000 times of the ‘‘correct’’ LR.

The use of an inappropriate allele database did not,

however, have that much influence on the error rates. More

relatives of the TF were included as the TF using Swedish

allele data compared with the correct allele frequencies. For

instance, 2.5 times more brothers were included as the TF

using Swedish (3.1% included brothers), instead of Rwandan

(1.2%) allele frequencies using 99.99% as a cutoff. The

exclusion error was lowered using an inappropriate

frequency database making little change in the total error

rate.

3.4. Five hypotheses model

As explained in the materials and methods sections, we can

use a more refined prior, using five different pedigree

hypotheses. This approach reduced both the exclusion and

the inclusion error rates both when the hypotheses were

considered individually and all together (Table 1, Fig. 5). Using

appropriate cutoff values (99.99% for the two hypotheses

model and 50% for the five hypotheses model) the total error

rate was significantly reduced.

Fig. 5. Receiver operating characteristics (ROC) of the relation between the

exclusion and the inclusion error rates using the two hypotheses standard model

and the five hypotheses model.

migration cases: The risk of erroneous conclusions, Forensic Sci. Int.

Table 1

Error rates using the standard two hypotheses model and the five hypotheses model

Simulated alleged father Error rate (%, (S.D. (95%))) P-Value

Two hypotheses model (99.99% cutoff) Five hypotheses model (50% cutoff)

True father (TF)a 0.94 (0.19) 0.65 (0.16) 0.02

Brother of TFa 1.22 (0.22) 0.92 (0.19) 0.04

Father of TFa 1.05 (0.20) 0.96 (0.19) 0.50

Half-brother of TFa 0.01 (0.02) 0.03 (0.03) –

Unrelated to TFa 0 0 –

Exclusion errora 0.94 (0.19) 0.65 (0.16) 0.02

Inclusion error (mean)b 0.57 (0.07) 0.48 (0.07) 0.07

Total errorc 1.51 (0.11) 1.11 (0.09) 0.006

a Based on 10,000 simulations.b Based on 40,000 simulations.c Based on 50,000 simulations.

A.O. Karlsson et al. / Forensic Science International xxx (2007) xxx–xxx 5

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4. Discussion

We used pedigrees and simulated DNA profiles to investigate

inclusion/exclusion error rates, the impact of different mutation

models and inappropriate databases in immigration casework

statistics. We also suggest the use of a prior with a five hypotheses

model for probability computations. The use of DNA analysis in

family reunification is increasing and an evaluation of the

statistical methods used is important. Our results apply to the

overall operating characteristics, i.e., how certain rules and

procedures affect error rates on an average.

The two types of error rates investigated consisted of TF

excluded as the TF (exclusion error) and a non-true father

included as the TF (inclusion error). The weighing between

exclusion and inclusion errors is ultimately a legal and political

question. Traditional methods tend to result in roughly minimal

sum of error rates for the two types of errors under some

assumptions, indicating that in practice the two types of errors

have been considered equally costly. However, the ‘‘cost’’ of

splitting up a family because of genetical coincidences could

easily be considered much higher than the cost to society of

admitting some extra persons not legally entitled to entry.

For the inclusion error we chose to report the mean of the

different errors these rates consist of. We then assume that all

the different hypotheses H1a–H1d are equally likely to occur

when the AF is not the TF, an assumption most probably not

true, but since we do not know their actual proportions we chose

to treat them equally.

Simulating profiles with 25 STR markers, instead of the 15

markers, greatly reduced the error rates, especially the

exclusion error. Typing of 25 different loci is today possible,

but a reliable mutation model is required, since the chance of

mutations increases as more markers are used. Furthermore,

more markers will also increase the possibility of being linked

or to be in linkage disequilibrium, which will make it hard to

use the product role for independent markers.

Families with more than one child included in the pedigrees

have lower error rates, but in these cases there are some

important special considerations. For instance, the number of

possible pedigrees will expand rapidly with the number of

children, as the children may have different fathers.

Please cite this article in press as: A.O. Karlsson et al., DNA-testing for im

(2007), doi:10.1016/j.forsciint.2006.12.015

To account for inconsistencies the use of a mutation model

was in most cases better than not to use one even if m-gen and

m-comp differed. As mentioned above, mutations are not of

special interests in immigration casework but since these have

an impact on inclusion/exclusion error rates the data from such

simulations was presented. Our aim of this study was, however,

not to propose a mutation model, but to see how the error rates

were affected by different mutation rates excluding the risk that

our results are only valid with the mutation model we have

chosen to use.

In immigration casework we often have to rely on

inappropriate allele frequency databases, an issue that has

been discussed before [15] and also recently during the

identification of the tsunami victims [16]. However, our

calculations using different databases showed limited effects on

the error rates although the impact on computed likelihoods

could be quite large in individual cases. This difference in

likelihood ratios is most probably due to the frequency of the

paternal allele being typically lower in the Swedish database

compared with a more appropriate one. Pronounced differences

will also occur if an allele has never been observed in the

database. In a simple case where the paternal allele is known the

ratio (using Swedish allele frequencies compared with the

‘‘real’’) between the likelihood ratios could be given as:

LRSwe

LRCorrect

¼ pcorrecti

pswei

where pcorrecti is the paternal allele frequency, or average if

ambiguous, for locus i in the correct population and pswei is the

frequency, or average if ambiguous, in the Swedish database.

The total ratio will then be

LRSwe

LRCorrect

¼Y15

i¼1

pcorrecti

pswei

For example if a number of alleles are relatively common in

a given population and rare, or missing, in the Swedish

population the ratio between the likelihood ratios will be highly

affected. The opposite is less likely to occur and thus the

likelihood ratio will be greater than one.

migration cases: The risk of erroneous conclusions, Forensic Sci. Int.

A.O. Karlsson et al. / Forensic Science International xxx (2007) xxx–xxx6

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Changing (increasing) the cutoff value can be a good idea in

such cases, as it restores a more even balance between

exclusion and inclusion error rates, and lowers the total error

rate. However, the total error rate will still be higher than when

using correct allele frequencies. The use of a weighted mean of

calculated likelihoods, based on frequencies from different

population databases, has been proposed for uncertain

population affiliation [17].

The Swedish Migration Board claims that there are cases

where the AF has been shown, by other means, to be the brother

or some other close relative to the TF. Simulations confirmed

that such a sibship has a considerable impact, especially in the

context of using an inappropriate allele database and no

mutation model. Adding more hypotheses, consisting of

relatives to the TF, slightly reduced both the exclusion and

the inclusion errors. Since the posteriors for the three cases of

close relatives of TF (brother, father and half-brother of TF) are

similar, we considered reporting the sum of the four ‘‘non-

paternity’’ hypotheses (H1a–H1d) probabilities as a standard.

This sum is based on the fact that if the AF is not the TF one of

the other four hypotheses is true with equal probabilities. The

correct proportions of these alternative hypotheses are not

known and the used approach is fair for illustration.

The laboratory work does not differ between immigration

casework and paternity testing. There are however differences in

how to transform the DNA information into probability numbers.

Immigration casework is about collecting information such as

knowledge about the family constellation, population affiliation

and also including as many more children as possible. In many

cases these opportunities are not available. Our study showed,

however, that although information is missing, these cases can

often be correctly interpreted if valid methods and strategies are

used for the likelihood computations.

Acknowledgement

This study was partly supported by The Swedish Foundation

for Strategic Research.

Please cite this article in press as: A.O. Karlsson et al., DNA-testing for im

(2007), doi:10.1016/j.forsciint.2006.12.015

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